A satellite navigation system is a satellite based radio-navigation system in which a plurality of satellites orbit the earth and broadcast information that can be used by receivers to determine a position relative to the satellites. Example satellite navigation systems include the global positioning system (GPS), the GLONASS system, the COMPASS system, and the Galileo positioning system.
A satellite navigation system receiver (also referred to herein as simply “receiver”) can determine a navigation solution (e.g., position and/or velocity) based on pseudoranges to a plurality of navigation satellites. A pseudorange can be determined based on the time it takes for a signal to propagate from a navigation satellite to the receiver and the position of the satellite when it transmitted the signal. For each satellite visible to the receiver, a pseudorange can be calculated. Once the receiver has determined the distances (pseudoranges) between itself and multiple satellites, the receiver can calculate a position by triangulation using the known location of the multiple satellites. The precision of the location calculation increases as more satellites from which a pseudorange can be calculated increases. Due to limited processing capabilities, however, many receivers are limited to calculating a location based on a maximum number of satellites. For example, a receiver may be limited to calculating a location based on 5 satellites. Oftentimes, however, more than 5 satellites are visible to the receiver. Accordingly, such receivers are configured to select a sub-set of the visible satellites to use when calculating a location.
In some examples, such a receiver determines which sub-set of satellites is the best to use based on the geometrical dilution of precision (GDOP) in each dimension of the receiver measurement. The GDOP is related to the relative position of the satellites. When the satellites are close together, the geometry is said to be weak and the geometrical dilution of precision (GDOP) is said to be high; when the satellites are far apart and rather equidistantly spaced, the geometry is said to be strong and the GDOP is said to be low. In order to select the sub-set with the lowest GDOP, the receiver will go through each possible grouping of sub-sets among the visible satellites.